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The parallelogram has the angle measures shown. Can you conclude that it is a rhombus, a rectangle, or a square? Explain.
A parallelogram is drawn with a horizontal diagonal from the left to right vertices. Each of the four angles formed by a side and the diagonal at the left or right vertex is 72 degrees.
Based on the given information, we cannot conclude that the parallelogram is a rhombus, a rectangle, or a square.
A rhombus is a special type of parallelogram where all four sides are equal in length. This information about side lengths is not given.
A rectangle is a special type of parallelogram where all four angles are right angles, or 90 degrees. The given information tells us that the angles formed by a side and the diagonal are each 72 degrees, so we cannot conclude that the parallelogram is a rectangle.
A square is a special type of parallelogram where all four sides are equal in length and all four angles are right angles. Again, the given information does not provide any information about side lengths or right angles, so we cannot conclude that the parallelogram is a square.
In summary, without additional information, the given angle measures do not allow us to determine if the parallelogram is a rhombus, a rectangle, or a square.